1. Splash Screen

2. Lesson Menu Five-Minute Check (over Chapter 4) Then/Now New Vocabulary Theorems: Perpendicular Bisectors Example 1: Use the Perpendicular Bisector Theorems Theorem 5.3: Circumcenter Theorem Proof: Circumcenter Theorem Example 2: Real-World Example: Use the Circumcenter Theorem Theorems: Angle Bisectors Example 3: Use the Angle Bisector Theorems Theorem 5.6: Incenter Theorem Example 4: Use the Incenter Theorem

3. Over Chapter 4 5-Minute Check 1 A.scalene B.isosceles C.equilateral Classify the triangle. A.A B.B C.C

4. Over Chapter 4 A.A B.B C.C D.D 5-Minute Check 2 A.3.75 B.6 C.12 D.16.5 Find x if m  A = 10x + 15, m  B = 8x – 18, and m  C = 12x + 3.

5. Over Chapter 4 5-Minute Check 3 A.  R   V,  S   W,  T   U B.  R   W,  S   U,  T   V C.  R   U,  S   V,  T   W D.  R   U,  S   W,  T   V Name the corresponding congruent sides if ΔRST  ΔUVW. A.A B.B C.C

6. Over Chapter 4 5-Minute Check 4 Name the corresponding congruent sides if ΔLMN  ΔOPQ. A.A B.B C.C A. B. C. D.,

7. Over Chapter 4 A.A B.B C.C D.D 5-Minute Check 5 A.22 B.10.75 C.7 D.4.5 Find y if ΔDEF is an equilateral triangle and m  F = 8y + 4.

8. Then/Now You used segment and angle bisectors. (Lesson 1–3 and 1–4) Identify and use perpendicular bisectors in triangles. Identify and use angle bisectors in triangles.

9. Vocabulary perpendicular bisector

10. Concept

11. Example 1 Use the Perpendicular Bisector Theorems A. Find the measure of BC. Answer: 8.5 BC= ACPerpendicular Bisector Theorem BC= 8.5Substitution

12. Example 1 Use the Perpendicular Bisector Theorems B. Find the measure of XY. Answer: 6

13. Example 1 Use the Perpendicular Bisector Theorems C. Find the measure of PQ. PQ= RQPerpendicular Bisector Theorem 3x + 1= 5x – 3Substitution 1= 2x – 3Subtract 3x from each side. 4= 2xAdd 3 to each side. 2= xDivide each side by 2. So, PQ = 3(2) + 1 = 7. Answer: 7

14. A.A B.B C.C D.D Example 1 A.4.6 B.9.2 C.18.4 D.36.8 A. Find the measure of NO.

15. A.A B.B C.C D.D Example 1 A.2 B.4 C.8 D.16 B. Find the measure of TU.

16. A.A B.B C.C D.D Example 1 A.8 B.12 C.16 D.20 C. Find the measure of EH.

17. Concept

18. Example 3 Use the Angle Bisector Theorems A. Find DB. Answer: DB = 5 DB= DCAngle Bisector Theorem DB= 5Substitution

19. Example 3 Use the Angle Bisector Theorems B. Find  WYZ.

20. Example 3 Use the Angle Bisector Theorems Answer: m  WYZ = 28  WYZ   XYZDefinition of angle bisector m  WYZ= m  XYZDefinition of congruent angles m  WYZ= 28Substitution

21. Example 3 Use the Angle Bisector Theorems C. Find QS. Answer: So, QS = 4(3) – 1 or 11. QS= SRAngle Bisector Theorem 4x – 1= 3x + 2Substitution x – 1= 2Subtract 3x from each side. x= 3Add 1 to each side.

22. A.A B.B C.C D.D Example 3 A.22 B.5.5 C.11 D.2.25 A. Find the measure of SR.

23. A.A B.B C.C D.D Example 3 A.28 B.30 C.15 D.30 B. Find the measure of  HFI.

24. A.A B.B C.C D.D Example 3 A.7 B.14 C.19 D.25 C. Find the measure of UV.

25. Splash Screen

26. Vocabulary median altitude

27. Altitude:Altitude: (of a triangle) is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. Median:Median: (of a triangle) is a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side.

28. Concept

29. End of the Lesson